To reduce the amount of data of a multi-channel audio signal with three or more channels, methods of coding an audio signal have been developed. Of these, one coding method standardized by the Moving Picture Experts Group (MPEG) is known as the MPEG Surround method. In the MPEG Surround method, a 5.1-channel audio signal to be coded undergoes time-frequency conversion and the frequency signal resulting from the time-frequency conversion is down-mixed, creating a three-channel frequency signal. When the three-channel frequency signal is down-mixed again, a frequency signal corresponding to a two-channel stereo signal is calculated. The frequency signal corresponding to the stereo signal is coded by the Advanced Audio Coding (AAC) method and Spectral Band Replication (SBR) method. In the MPEG Surround method, spatial information, which indicates spread or localization of sound is calculated at the time when the 5.1-channel signal is down-mixed to the three-channel signal and when the three-channel signal is down-mixed to the two-channel signal, after which the spatial information is coded. Accordingly, in the MPEG Surround method, a stereo signal resulting from down-mixing a multi-channel audio signal and spatial signal with a relatively small amount of data are coded. Therefore, the MPEG Surround method achieves higher compression efficiency than when a signal in each channel included in a multi-channel audio signal is independently coded.
In the MPEG Surround method, spatial information calculated at the creation of a stereo frequency signal is coded by using channel prediction coefficients. The channel prediction coefficients are used to perform predictive coding on a signal in one of three channels according to signals in the remaining two channels. A plurality of channel prediction coefficients are stored in a table, which is a so-called coding book. The coding book is used to improve the efficiency of the bit rate in use. When a coder and a decoder share a common predetermined coding book (or they each have a coding book created by a common method), it becomes possible to transmit more important information with less bits. At the time of decoding, the signal in one of the three channels is replicated according to the channel prediction coefficient described above. Therefore, it is desirable to select an optimum channel prediction coefficient from the code book at the time of coding.
In an disclosed method of selecting an optimum channel prediction coefficient from the code book, error defined by a difference between a channel signal before predictive coding and a channel signal resulting from the predictive coding is calculated by using each of all channel prediction coefficients stored in the code book, and a channel prediction coefficient that minimizes the error in predictive coding is selected. A technology to calculate a channel prediction coefficient that minimizes error by using the least squares method is also disclosed in Japanese Laid-open Patent Publication No. 2008-517338.